Substitute Xherdan Shaqiri scored twice as Liverpool cruised back to the top of the Premier League with a 3-1 win over Manchester United at Anfield.

Sadio Mane had given Liverpool a first-half lead but United levelled through Jesse Lingard before the break, and against the run of play, following an error from Allison before Shaqiri took over.

The game -- in which Liverpool registered 36 shots to United's six -- began at a frantic pace, the home side needing only three minutes to register their first attempt when Mohamed Salah set up Roberto Firmino, whose shot was deflected wide.

A minute later, United had the ball in the net when a free kick from the left flew through the area and in but Romelu Lukaku, standing close to Alisson and swinging a foot at the ball as it passed, was offside.

Firmino glanced a header wide as Liverpool returned to the attack and, with the 10-minute mark still to be reached, United keeper David De Gea tipped away another effort from the same player.

De Gea was involved again as he repelled a Fabinho strike, Ashley Young hacking clear from close to his own goal-line when the resulting corner came in.

Fabinho had another go, this time smacking a strike well over from distance, as Liverpool continued their early dominance with United struggling to keep possession.

Salah won another corner for the home side as the pace began to slow slightly around the 20-minute mark, but it came to nothing as United's Marcus Rashford, back helping out his defenders, was fouled for a free kick.

But five minutes later, Liverpool were deservedly in front as Fabinho lofted a sublime pass to Mane, bursting into the area, who controlled the ball and steered it past De Gea.

United were looking ragged and Diogo Dalot went into the book for fouling Andrew Robertson as he burst down the left, the resulting free kick falling to Dejan Lovren who was unable to steer it in from close range under pressure.

Lukaku, bereft of support, squeezed in a low cross that was easily cleared as the visitors tried to hit back -- but they levelled against the run of play after 33 minutes when Alisson allowed another Lukaku cross to slip from his grasp and Lingard pounced.

The goal changed the mood inside Anfield, the previously buoyant home crowd stunned, with Mane trying to lift them again only to see his shot from distance easily dealt with by De Gea.

Lukaku was booked for a crunching challenge on Naby Keita, but Liverpool were struggling to rediscover their rhythm as Firmino lost the ball and was lucky not to get booked for racing back to foul Rashford as the visitors broke.

Alisson held on as Ander Herrera shot from outside the area with the first half moving into its final five minutes, Fabinho following that lead with a long-range effort that deflected wide moments later.

United manager Jose Mourinho made a change at the break, bringing on Marouane Fellaini for Dalot and switching to a 4-3-3, but Liverpool began the second half with the greater purpose and Herrera was booked for fouling Salah.

The home side were close to restoring their lead after 52 minutes when De Gea made a fine stop after Firmino skipped away from defenders and steered a shot goalwards.

As the hour approached, Lovren ventured forward to lash a long-range shot high into the Kop, and then defensive colleague Virgil van Dijk's attempt cannoned to safety.

United briefly broke out to create a threat of their own, Robertson intervening when a cross seemed destined for Fellaini, but the corner came to nothing.

Georginio Wijnaldum's shot through a crowd was fielded by De Gea, and with 20 minutes to go Jurgen Klopp made a change, bringing on Shaqiri for Naby Keita.

De Gea was again unflappable when Fabinho tried his luck from range, and at the other end Lingard made a good run down the left only to overhit a cross beyond Lukaku.

But with 17 minutes remaining, De Gea was beaten again as Mane got free on the left and made his way into the area. When the United keeper scrambled the ball away it fell to Shaqiri, whose effort took a deflection off Young on its way in off the bar.

With Paul Pogba continuing to look on from the bench, Lingard fired wildly over for United -- and when Mourinho made his next change, he brought on Anthony Martial for Herrera.

But with 10 minutes remaining, the game was over when Shaqiri's strike from the edge of the area took a big deflection off Eric Bailly to leave De Gea with no chance.

Liverpool replaced Mane with Jordan Henderson, United opting to swap Lingard for Juan Mata as the home side eased to the victory that lifted them back to the summit.